Optimization of flagellar swimming by a model sperm

TL;DR

This paper models sperm-like swimming using a bead-spring chain in viscous fluid, identifying optimal planar flagellar strokes through eigenvalue analysis, and applying these findings to simulate large amplitude swimming.

Contribution

It introduces a method to determine optimal flagellar strokes for a sperm model using eigenvalue analysis and applies these to simulate large amplitude swimming.

Findings

Optimal planar flagellar strokes can be identified via eigenvalue problems.

Nearly optimal actuating forces for elastic chains with cargo constraints are determined.

Simulation of large amplitude swimming using derived optimal strokes is feasible.

Abstract

The swimming of a bead-spring chain in a viscous incompressible fluid as a model of a sperm is studied in the framework of low Reynolds number hydrodynamics. The optimal mode in the class of planar flagellar strokes of small amplitude is determined on the basis of a generalized eigenvalue problem involving two matrices which can be evaluated from the mobility matrix of the set of spheres constituting the chain. For an elastic chain with a cargo constraint for its spherical head, the actuating forces yielding a nearly optimal stroke can be determined. These can be used in a Stokesian dynamics simulation of large amplitude swimming.